求证sin^4+cos^4=1-1/2sin^2(2α)

问题描述:

求证sin^4+cos^4=1-1/2sin^2(2α)

sinα^4+cosα^4=(sinα^2+cosα^2)^2-2sinα^2cosα^2=1^2-2(sinα^2cosα^2)=1-1/2(sin2α)^2